Welcome to the chicken and rabbit cage problem! This is a fun puzzle that helps us practice counting and thinking. In our cage, we have chickens and rabbits living together. Each chicken has 2 legs, and each rabbit has 4 legs. The challenge is: if we know how many animals are in the cage and how many legs there are in total, can we figure out exactly how many chickens and how many rabbits we have? Let's solve this mystery together!
Let's learn about the legs! This is very important for solving our puzzle. Look at the chicken on the left. A chicken has exactly 2 legs. Let's count them together: 1, 2! Now look at the rabbit on the right. A rabbit has 4 legs. Let's count: 1, 2, 3, 4! Remember this: chickens have 2 legs, rabbits have 4 legs. This difference in the number of legs is the key to solving our puzzle!
Now let's solve a real example together! We have 5 animals in the cage and 14 legs in total. We need to find how many chickens and how many rabbits there are. Let's try different combinations. What if we have 3 chickens and 2 rabbits? Let's count the legs: 3 chickens times 2 legs each equals 6 legs. Plus 2 rabbits times 4 legs each equals 8 legs. So 6 plus 8 equals 14 legs total. Perfect! That matches our problem. So the answer is 3 chickens and 2 rabbits!
Now I'll teach you a magic trick to solve these problems quickly! Here's the secret: first, pretend ALL animals are chickens. In our example with 5 animals, if they were all chickens, we'd have 5 times 2 equals 10 legs. But we actually have 14 legs, so we have 4 extra legs. Here's the magic: every time we change a chicken into a rabbit, we get 2 extra legs. So we need to change 2 chickens into rabbits. Watch the magic happen! Now we have 3 chickens and 2 rabbits, which gives us exactly 14 legs!
Great! Now let's practice together with a new problem. We have 8 animals and 22 legs total. Let's use our magic trick method! Step 1: Pretend all 8 animals are chickens. That gives us 8 times 2 equals 16 legs. Step 2: We need 22 legs total, so we have 22 minus 16 equals 6 extra legs. Step 3: Each rabbit gives us 2 extra legs, so we need 6 divided by 2 equals 3 rabbits. Watch as we transform 3 chickens into rabbits! So our answer is 5 chickens and 3 rabbits. Let's check: 5 times 2 plus 3 times 4 equals 10 plus 12 equals 22. Perfect! You did it!